Scanning optical apparatus

ABSTRACT

A scanning optical apparatus for a printer and a digital copying machine has a light source, a deflector, first and second imaging units. The deflector deflects a light beam emitted from the light source to a main scanning direction. The first imaging unit makes the light beam emitted from the light source form an image in the vicinity of the deflection position of said deflector in the sub-scanning direction. The first imaging unit has a first resin lens having a negative refractive power only in a sub-scanning direction. The second imaging unit makes the light beam deflected by the deflector form an image on a scanned surface in the sub-scanning direction. The second imaging unit has a second resin lens having a positive refractive power only in the sub-scanning direction.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a scanning optical apparatus, and morespecifically, to a scanning optical apparatus used as an image writingmeans for a printer and a digital copying machine.

2. Description of the Prior Art

The optical scanning apparatus has been frequently used as an imagewriting means for a printer and a digital copying machine. An example ofthe scanning optical apparatus will be described with reference to theperspective view of FIG. 1 and the optical path views of FIGS. 2A and2B.

Referring to FIG. 1, a conventional scanning optical apparatus 100includes a laser diode 2 serving as a light source, a polygonal mirror 3serving as a deflector, and a photoreceptor drum 4 serving as a surfaceto be scanned (hereinafter, referred to as "scanned surface"). Theoptical system generally includes a first imaging portion G101 which isfrom the laser diode 2 to the polygonal mirror 3 and a second imagingportion G102 which is from the polygonal mirror 3 to the photoreceptordrum 4.

Hereinafter, a direction parallel to a direction in which the lightbeams is directed will be referred to as an optical axis direction, adirection that is in a plane vertical to the optical axis direction andin which the light beam is deflected by the polygonal mirror 3 will bereferred to as a main scanning direction, and a direction which is in aplane vertical to the optical axis and is orthogonal to the mainscanning direction will be referred to as a sub-scanning direction.

The first imaging portion G101 includes from the light source side acollimator lens 5 having a positive refractive power, a plano-convexcylindrical lens 101 having a positive refractive power only in thesub-scanning direction and convex to the light source side, and a firstreflecting mirror 8.

The second imaging portion G102 includes from the light source side afirst scanning lens 9 which is a bi-concave lens having a negativerefractive power, a second scanning lens 10 which is a plano-convex lenshaving a positive refractive power and plane to the light source side, asecond reflecting mirror 11, and an image plane inclination correctinglens 102 which is a plano-convex cylindrical lens having a positiverefractive power only in the sub-scanning direction and convex to thelight source side.

Referring to FIGS. 2A and 2B, there is schematically shown an opticalpath of the conventional optical apparatus 100. FIG. 2A is across-sectional view of the optical path in the main scanning direction.FIG. 2B is a cross-sectional view of the path in the sub-scanningdirection. The construction data of the optical system of the laseroptical apparatus 100 are shown in Table 1. In the table, the firstsurface is the light source side surface of the cylindrical lens 101 andthe construction data of the collimator lens 5 are not shown. The laserbeam incident on the cylindrical lens 101 is a parallel beam.

                  TABLE 1                                                         ______________________________________                                        Construction Data of Conventional Apparatus                                   Radius of Radius of                                                           Curvature Curvature                                                                              Surface    Axial  Refractive                               (Y)       (Z)      Configuration                                                                            Distance                                                                             Index                                    ______________________________________                                         Cylindrical lens, made of glass, positive!                                   1   ∞   103.744  Y-cylinder                                                                             4.000  1.51118                                2   ∞   ←   Plane    200.303                                                                              1.00000                                 Deflection surface!                                                          5   ∞   ←   Plane    33.000 1.00000                                 Scanning lens!                                                               (G1, made of glass)                                                           6   -254.411  ←   Spherical                                                                              7.000  1.51118                                7   1098.901  ←   Spherical                                                                              30.440 1.00000                                (G2, made of glass)                                                           8   ∞   ←   Plane    15.000 1.82489                                9   -147.454  ←   Spherical                                                                              163.844                                                                              1.00000                                 Image plane inclination correcting lens, made of resin, positive!            10  ∞    44.590  Y-cylinder                                                                             5.000  1.48457                                11  ∞   ←   Plane    131.039                                                                              1.00000                                 Scanned surface!                                                             12  ∞   ←   Plane                                                  ______________________________________                                         * Light beam incident on the first surface is a parallel beam (object         distance is ∞).                                                    

In the scanning optical apparatus 100 shown in FIGS. 2A and 2B, thecollimator lens 5 shapes a laser beam emitted from the laser diode 2into a parallel beam with respect to the main and sub-scanningdirections. The laser beam exiting from the collimator lens 5 is, in themain scanning direction (see FIG. 2A), deflected by the polygonal mirror3 while maintaining its parallel state and imaged on the photoreceptordrum 4 by the refractive powers of the first and second scanning lenses9 and 10.

In the sub-scanning direction (see FIG. 2B), the laser beam from thecollimator lens 5 is imaged in the vicinity of the point of deflectionof the polygonal mirror 3 by the positive refractive power of thecylindrical lens 101 of the first imaging portion G101. Then, the laserbeam reflected by the polygonal mirror 3 passes through the first andsecond scanning lenses 9 and 10, is reflected by the second reflectingmirror 11, passes through the image plane inclination lens 102, and isre-imaged on the photoreceptor drum 4.

That is, with respect to the sub-scanning direction of the secondimaging portion G102, the vicinity of the point of deflection of thepolygonal mirror 3 and the image point on the photoreceptor drum 4 arein an optically conjugate relationship and the second imaging portionG102 forms a so-called image plane inclination correcting opticalsystem.

In recent years, there has been a demand that printers and digitalcopying machines have higher pixel density. Accordingly, in the scanningoptical apparatus used in an image writing portion of the image formingapparatus, the permissible range of the size and position of the spotdiameter on the photoreceptor drum tends to decrease. In addition, inorder to obtain images of excellent quality, it is necessary to reducethe permissible range of the size and position of the spot diameter notonly in the main scanning direction but also in the sub-scanningdirection. For this reason, an image plane inclination correctingoptical system is required to have a high correcting capability.

In order to obtain a high correcting capability in the image planeinclination correcting optical system, the magnification of the secondimaging portion G102 is reduced by increasing the sub-scanning directionrefractive powers of the first and second scanning lenses or bydisposing the image plane inclination correcting lens 102 closer to thephotoreceptor drum 4. If the magnification of the second imaging portionG102 is reduced, even if the point of deflection largely shifts in thesub-scanning direction, the generation of an incomplete image caused byan image plane inclination in the sub-scanning direction will not beremarkable since the second imaging portion G102 acts to reduce theerror of shift of the spot on the photoreceptor drum 4.

However, if the magnification of the second imaging portion G102 isreduced in the image plane inclination correcting optical system, aproblem arises due to an elongation of the image plane inclinationcorrecting lens 102 as described below.

For the magnification reduction of the second imaging portion G102, themethod of increasing the sub-scanning direction refractive powers of thefirst and second scanning lenses 9 and 10 is undesirable. This isbecause the scanning lens having a high refractive power in thesub-scanning direction cannot be formed of spherical surfaces havingequal refractive powers in the main and sub-scanning directions becauseof magnification limitations in the main scanning direction, and the useof the anamorphic lens for this reason increases the cost. Therefore,for the magnification reduction of the second imaging portion G102, themethod of disposing the image plane inclination lens 102 closer to theimage side (to the photoreceptor drum 4) is preferred.

When the image plane inclination correcting lens 102 is disposed closerto the image side (to the photoreceptor drum 4), to cover the scanningwidth, the image plane inclination correcting lens 102 is elongated inthe main scanning direction. It is preferred that such an elongate lensis made of resin since if it is made of glass, the manufacture cost willincreases.

In resin, however, the variation in refractive index and configurationdue to a variation in temperature is greater than in glass. For thisreason, if a lens having a great refractive power such as the imageplane inclination correcting lens 102 is made of resin, the effect ofvariation in the refractive power due to environmental changes cannot beignored, so that the variation in spot diameter on the scanned surfacewill increase.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a scanning opticalapparatus in which the spot diameter of the light beam on the scannedsurface does not vary even if the environmental temperature varies.

According to one feature of the present invention, a scanning opticalapparatus is provided with a light source, a deflector for deflecting alight beam emitted from the light source to a main scanning direction, afirst imaging unit including a first resin lens having a negativerefractive power only in a sub-scanning direction perpendicular to themain scanning direction for making the light beam emitted from the lightsource form an image in the vicinity of the deflection position of saiddeflector in the sub-scanning direction, and a second imaging unitincluding a second resin lens having a positive refractive power only inthe sub-scanning direction for making the light beam deflected by thedeflector form an image on a scanned surface in the sub-scanningdirection.

According to another feature of the present invention, a scanningoptical apparatus is provided with a light source, a deflector fordeflecting a light beam emitted from the light source in a main scanningdirection, a first lens and a second lens arranged between the lightsource and the deflector, and a supporting unit for supporting the firstand the second lenses, including a base, a first supporting member forsupporting the first lens, and a second supporting member for supportingthe second lens, and it is characterized in that the second supportingmember can be fixed at any given position with respect to the base, andin that the first supporting member can be fixed both at any givenposition in an optical axis direction and at any angle about the opticalaxis with respect to the second supporting member.

According to a further feature of the present invention, a scanningoptical apparatus is provided with a light source, an objective lensunit for condensing a light beam emitted from said light source, a firstimaging unit for converging the light beam having passed through saidobjective lens unit in a sub-scanning direction, a deflector arranged ator in the vicinity of an image formation position of the light beamhaving passed through said first imaging unit, and a second imaging unitfor making the light beam deflected by said deflector to form an imageon a scanned surface and for maintaining a conjugate relation betweensaid reflector and said scanned surface in a sub-scanning section, andit is characterized in that said objective lens unit condenses the lightbeam from said light source so that the condensed light beam is directedto said second imaging unit in a main scanning direction, in that saidfirst imaging unit, having a refractive power only in the sub-scanningdirection, comprising a glass lens having a positive refractive power inthe sub-scanning direction and a resin lens having a negative refractivepower in the sub-scanning direction, has as a whole a positiverefractive power in the sub-scanning direction, and in that all lenscomponents in said second imaging unit are made of resin, an overallrefractive power thereof in the main scanning direction beingsubstantially null.

According to a still further feature of the present invention, ascanning optical apparatus is provided with a light source, an objectivelens unit for condensing a light beam emitted from said light source, afirst imaging unit including a first resin lens having a negativerefractive power in a sub-scanning direction yet having no refractivepower in a main scanning direction for making the light beam havingpassed through said group of lenses converge in the sub-scanningdirection, a deflector arranged at or in the vicinity of an imageformation position of the light beam having passed through said firstimaging unit, a second imaging unit including a second resin lens havinga positive refractive power in the sub-scanning direction yet having norefractive power in the main scanning direction for making the lightbeam deflected by said deflector form an image on a scanned surface andfor maintaining a subjugate relation between said deflector and saidscanned surface in a sub-scanning section.

BRIEF DESCRIPTION OF THE DRAWINGS

This and other objects and features of this invention will become clearfrom the following description, taken in conjunction with the preferredembodiments with reference to the accompanied drawings in which:

FIG. 1 is a perspective view showing the optical system of theconventional scanning optical apparatus;

FIGS. 2A and 2B are optical path views showing the optical system of theconventional scanning optical apparatus;

FIG. 3 is a schematic view showing the refractive power arrangement ofthe conventional scanning optical apparatus in the sub-scanningdirection;

FIGS. 4A and 4B are optical path views showing an optical system of ascanning optical apparatus of the present invention;

FIG. 5 is a schematic view showing the refractive power arrangement ofthe present invention in the sub-scanning direction;

FIGS. 6A, 6B and 6C show an example of a manner of holding first andsecond cylindrical lenses;

FIGS. 7A, 7B, 7C and 7D show another example of the manner of holdingthe first and second cylindrical lenses;

FIG. 8A is a cross-sectional view schematically showing the refractivepower arrangement and optical path of the present invention in the mainscanning direction;

FIG. 8B is a cross-sectional view schematically showing the refractivepower arrangement and optical path of the present invention in thesub-scanning direction;

FIGS. 9A, 9B and 9C are views of assistance in explaining an effect onthe back focal length in the present invention;

FIGS. 10A and lOB are cross-sectional views in the sub-scanningdirection schematically showing the refractive power arrangement andoptical path to explain temperature compensation by comparing a generallaser scanning optical system and a laser scanning optical system of thepresent invention;

FIGS. 11A and 11B are views of assistance in explaining an effect on thelens arrangement of an anamorphic lens included in the presentinvention;

FIG. 12 is a cross-sectional view in the main scanning direction showingthe lens arrangement and optical path from a deflective reflectionsurface to a scanned surface in an embodiment of the present inventionand an example for comparison with the embodiment;

FIG. 13 is a cross-sectional view in the sub-scanning direction showingthe lens arrangement and optical path from the anamorphic lens to thescanned surface in the embodiment of the present invention;

FIG. 14 is a cross-sectional view in the sub-scanning direction showingthe lens arrangement and optical path from the anamorphic lens to thedeflective reflection surface in the embodiment of the presentinvention;

FIG. 15 is a cross-sectional view in the sub-scanning direction showingthe lens arrangement and optical path from the anamorphic lens to thescanned surface in the example for comparison; and

FIG. 16 is a cross-sectional view in the sub-scanning direction showingthe lens arrangement and optical path from the anamorphic lens to thedeflective reflection surface in the example for comparison.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIGS. 4 to 7 show a first implementation of the present invention.Hereinafter, embodiments of a scanning optical apparatus of the firstimplementation will be described.

Referring to FIGS. 4A and 4B, there is schematically shown an opticalpath of a scanning optical apparatus 1 of the present invention. FIG. 4Ais a cross-sectional view of the optical path in the main scanningdirection. FIG. 4B is a cross-sectional view of the optical path in thesub-scanning direction. The construction data of first to sixthembodiments employing the arrangement of the optical apparatus 1 areshown in Tables 2 to 7. In the tables, the construction data of thecollimator lens are not shown like in Table 1. The laser beam incidenton a cylindrical lens 6 is a parallel beam.

                  TABLE 2                                                         ______________________________________                                        Construction Data of 1st Embodiment                                           Radius of Radius of                                                           Curvature Curvature                                                                              Surface    Axial  Refractive                               (Y)       (Z)      Configuration                                                                            Distance                                                                             Index                                    ______________________________________                                         Cylindrical lens, made of glass, positive!                                   1   ∞   12.780   Y-cylinder                                                                             3.000  1.51118                                2   ∞   ←   Plane    12.783 1.00000                                 Cylindrical lens, made of resin, negative!                                   3   ∞   ←   Plane    2.200  1.48457                                4   *         4.846    Y-cylinder                                                                             70.002 1.00000                                 Deflection surface!                                                          5   ∞   ←   Plane    33.000 1.00000                                 Scanning lens!                                                               (G1, made of glass)                                                           6   -254.411  ←   Spherical                                                                              7.000  1.51118                                7   1098.901  ←   Spherical                                                                              30.440 1.00000                                (G2, made of glass)                                                           8   ∞   ←   Plane    15.000 1.82489                                9   -147.454  ←   Spherical                                                                              163.844                                                                              1.00000                                 Image plane inclination correcting lens, made of resin, positive!            10  ∞   44.590   Y-cylinder                                                                             5.000  1.48457                                11  ∞   ←   Plane    131.039                                                                              1.00000                                 Scanned surface!                                                             12  ∞   ←   Plane                                                  ______________________________________                                         * Light beam incident on the first surface is a parallel beam (object         distance is ∞).                                                    

                  TABLE 3                                                         ______________________________________                                        Construction Data of 2nd Embodiment                                           Radius of Radius of                                                           Curvature Curvature                                                                              Surface    Axial  Refractive                               (Y)       (Z)      Configuration                                                                            Distance                                                                             Index                                    ______________________________________                                         Cylindrical lens, made of glass, positive!                                   1   ∞   15.335   Y-cylinder                                                                             3.000  1.51118                                2   ∞   ←   Plane    12.933 1.00000                                 Cylindrical lens, made of resin, negative!                                   3   ∞   ←   Plane    2.200  1.48457                                4   ∞   7.753    Y-cylinder                                                                             91.469 1.00000                                 Deflection surface!                                                          5   ∞   ←   Plane    33.000 1.00000                                 Scanning lens!                                                               (G1, made of glass)                                                           6   -254.411  ←   Spherical                                                                              7.000  1.51118                                7   1098.901  ←   Spherical                                                                              30.440 1.00000                                (G2, made of glass)                                                           8   ∞   ←   Plane    15.000 1.82489                                9   -147.454  ←   Spherical                                                                              163.844                                                                              1.00000                                 Image plane inclination correcting lens, made of resin, positive!            10  ∞   44.590   Y-cylinder                                                                             5.000  1.48457                                11  ∞   ←   Plane    131.039                                                                              1.00000                                 Scanned surface!                                                             12  ∞   ←   Plane                                                  ______________________________________                                         * Light beam incident on the first surface is a parallel beam (object         distance is ∞).                                                    

                  TABLE 4                                                         ______________________________________                                        Construction Data of 3rd Embodiment                                           Radius of Radius of                                                           Curvature Curvature                                                                              Surface    Axial  Refractive                               (Y)       (Z)      Configuration                                                                            Distance                                                                             Index                                    ______________________________________                                         Cylindrical lens, made of glass, positive!                                   1   ∞   17.891   Y-cylinder                                                                             3.000  1.51118                                2   ∞   ←   Plane    10.907 1.00000                                 Cylindrical lens, made of resin, negative!                                   3   ∞   ←   Plane    2.200  1.48457                                4   ∞   12.114   Y-cylinder                                                                             118.663                                                                              1.00000                                 Deflection surface!                                                          5   ∞   ←   Plane    33.000 1.00000                                 Scanning lens!                                                               (G1, made of glass)                                                           6   -254.411  ←   Spherical                                                                              7.000  1.51118                                7   1098.901  ←   Spherical                                                                              30.440 1.00000                                (G2, made of glass)                                                           8   ∞   ←   Plane    15.000 1.82489                                9   -147.454  ←   Spherical                                                                              163.844                                                                              1.00000                                 Image plane inclination correcting lens, made of resin, positive!            10  ∞   44.590   Y-cylinder                                                                             5.000  1.48457                                11  ∞   ←   Plane    131.039                                                                              1.00000                                 Scanned surface!                                                             12  ∞   ←   Plane                                                  ______________________________________                                         * Light beam incident on the first surface is a parallel beam (object         distance is ∞).                                                    

                  TABLE 5                                                         ______________________________________                                        Construction Data of 4th Embodiment                                           Radius of Radius of                                                           Curvature Curvature                                                                              Surface    Axial  Refractive                               (Y)       (Z)      Configuration                                                                            Distance                                                                             Index                                    ______________________________________                                         Cylindrical lens, made of glass, positive!                                   1   ∞   20.447   Y-cylinder                                                                             3.000  1.51118                                2   ∞   ←   Plane    8.533  1.00000                                 Cylindrical lens, made of resin, negative!                                   3   ∞   ←   Plane    2.200  1.48457                                4   ∞   16.960   Y-cylinder                                                                             140.801                                                                              1.00000                                 Deflection surface!                                                          5   ∞   ←   Plane    33.000 1.00000                                 Scanning lens!                                                               (G1, made of glass)                                                           6   -254.411  ←   Spherical                                                                              7.000  1.51118                                7   1098.901  ←   Spherical                                                                              30.440 1.00000                                (G2, made of glass)                                                           8   ∞   ←   Plane    15.000 1.82489                                9   -147.454  ←   Spherical                                                                              163.844                                                                              1.00000                                 Image plane inclination correcting lens, made of resin, positive!            10  ∞   44.590   Y-cylinder                                                                             5.000  1.48457                                11  ∞   ←   Plane    131.039                                                                              1.00000                                 Scanned surface!                                                             12  ∞   ←   Plane                                                  ______________________________________                                         * Light beam incident on the first surf ace is a parallel beam (object        distance is ∞).                                                    

                  TABLE 6                                                         ______________________________________                                        Construction Data of 5th Embodiment                                           Radius of Radius of                                                           Curvature Curvature                                                                              Surface    Axial  Refractive                               (Y)       (Z)      Configuration                                                                            Distance                                                                             Index                                    ______________________________________                                         Cylindrical lens, made of glass, positive!                                   1   ∞   23.003   Y-cylinder                                                                             3.000  1.51118                                2   ∞   ←   Plane    6.658  1.00000                                 Cylindrical lens, made of resin, negative!                                   3   ∞   ←   Plane    2.200  1.48457                                4   ∞   21.806   Y-cylinder                                                                             155.804                                                                              1.00000                                 Deflection surface!                                                          5   ∞   ←   Plane    33.000 1.00000                                 Scanning lens!                                                               (G1, made of glass)                                                           6   -254.411  ←   Spherical                                                                              7.000  1.51118                                7   1098.901  ←   Spherical                                                                              30.440 1.00000                                (G2, made of glass)                                                           8   ∞   ←   Plane    15.000 1.82489                                9   -147.454  ←   Spherical                                                                              163.844                                                                              1.00000                                 Image plane inclination correcting lens, made of resin, positive!            10  ∞   44.590   Y-cylinder                                                                             5.000  1.48457                                11  ∞   ←   Plane    131.039                                                                              1.00000                                 Scanned surface!                                                             12  ∞   ←   Plane                                                  ______________________________________                                         * Light beam incident on the first surface is a parallel beam (object         distance is ∞).                                                    

                  TABLE 7                                                         ______________________________________                                        Construction Data of 6th Embodiment                                           Radius of Radius of                                                           Curvature Curvature                                                                              Surface    Axial  Refractive                               (Y)       (Z)      Configuration                                                                            Distance                                                                             Index                                    ______________________________________                                         Cylindrical lens, made of glass, positive!                                   1   ∞   25.559   Y-cylinder                                                                             3.000  1.51118                                2   ∞   ←   Plane    1.530  1.00000                                 Cylindrical lens, made of resin, negative!                                   3   ∞   ←   Plane    2.200  1.48457                                4   ∞   29.074   Y-cylinder                                                                             180.858                                                                              1.00000                                 Deflection surface!                                                          5   ∞   ←   Plane    33.000 1.00000                                 Scanning lens!                                                               (G1, made of glass)                                                           6   -254.411  ←   Spherical                                                                              7.000  1.51118                                7   1098.901  ←   Spherical                                                                              30.440 1.00000                                (G2, made of glass)                                                           8   ∞   ←   Plane    15.000 1.82489                                9   -147.454  ←   Spherical                                                                              163.844                                                                              1.00000                                 Image plane inclination correcting lens, made of resin, positive!            10  ∞   44.590   Y-cylinder                                                                             5.000  1.48457                                11  ∞   ←   Plane    131.039                                                                              1.00000                                 Scanned surface!                                                             12  ∞   ←   Plane                                                  ______________________________________                                         * Light beam incident on the first surface is a parallel beam (object         distance is ∞).                                                    

Referring to FIGS. 4A and 4B, since the arrangement of the scanningoptical apparatus 1 of the present invention is the same as that of thescanning optical apparatus 100 described in the description of the priorart, only different features will be described and detailed descriptionwill not be given.

In the scanning optical apparatus 1, a plano-convex first cylindricallens 6 (first lens) convex to the light source side and having arefractive power only in the sub-scanning direction and a plano-concavesecond cylindrical lens 7 (second lens) plane to the light source sideand having a refractive power only in the sub-scanning direction aredisposed in the position of the cylindrical lens 101 of the conventionalscanning optical apparatus 100. A plano-convex image plane inclinationcorrecting lens 12 convex to the light source side and having arefractive power only in the sub-scanning lens is disposed in theposition of the image plane inclination correcting lens 102 of theconventional scanning optical apparatus 100. In the scanning opticalapparatus 1, a first imaging portion G1 is from the laser diode 2 to thepolygonal mirror 3, and a second imaging portion G2 is from thepolygonal mirror 3 to the photoreceptor drum 4.

In the first to sixth embodiments of the present invention, the secondcylindrical lens 7 and the image plane inclination correcting lens 12(hatched in the figures) are made of resin and the other lenses are madeof glass.

In the scanning optical apparatus shown in FIGS. 4A and 4B, the laserbeam emitted from the laser diode 2 is shaped into a parallel beam bythe collimator lens 5.

In the main scanning direction, the laser beam (see FIG. 4A) is imagedon the photoreceptor drum 4 to scan its surface by the same manner as inthe optical path described with respect to the conventional apparatus.

On the other hand, in the sub-scanning direction, the laser beam (seeFIG. 4B) is imaged in the vicinity of the point of deflection of thepolygonal mirror 3 by the first cylindrical lens 6 and the secondcylindrical lens 7 and is re-imaged on the scanned surface by theoverall positive refractive power of the scanning lens including thefirst scanning lens 9 and the second scanning lens 10 and the positiverefractive power of the image plane inclination correcting lens 12. Thatis, the second imaging portion G2 also forms an image plane correctingoptical system.

According to the lens arrangement of the scanning optical apparatus 1(see FIGS. 4A and 4B), the total length of the first imaging portion canbe shorter than in the conventional scanning optical apparatus 100 (seeFIGS. 2A and 2B). That is, in order to image the parallel beam in thesub-scanning direction, the cylindrical lens 101 is used in the firstimaging portion G101 of the conventional apparatus, whereas in the firstimaging portion G1 of the present invention, the refractive power isdivided between the first cylindrical lens 6 and the second cylindricallens 7. With this lens arrangement, the lens principal pointcorresponding to the image on the deflection surface shifts toward thelight source side, so that the composite focal length of the firstcylindrical lens 6 and the second cylindrical lens 7 is reduced.

Generally, when the environmental temperature varies, lens materialsvary in configuration and refractive index. However, the variation ofresin in configuration and refractive index due to a variation intemperature is very great compared to that of glass. Therefore, to avariation in environmental temperature, in the case of the scanningoptical apparatus 1 of the embodiments of the present invention, thecontribution of the second cylindrical lens 7 and the image planeinclination correcting lens 12 is the greatest.

Specifically, when the environmental temperature varies, theconfiguration of the lens expands to reduce the refractive index, sothat the refractive powers of the second cylindrical lens 7 and theimage plane inclination correcting lens 12 vary according to thevariation in configuration and refractive index. For example, when theenvironmental temperature rises, the absolute values of refractivepowers of the second cylindrical lens 7 and the image plane inclinationcorrecting lens 12 decrease. However, since the signs of refractivepowers of the second cylindrical lens 7 and the image plane inclinationcorrecting lens 12 are opposite to each other, the variation inrefractive power of one of them compensates for the variation inrefractive power of the other. As a result, the variation in spotdiameter on the scanned surface is minimized.

In the scanning optical apparatus 1 of the present invention, such acompensation is effective only with respect to the sub-scanningdirection. With respect to the main scanning direction, the effect ofthe variation in environmental temperature is small since the lenseshaving refractive power in this direction are all made of glass.

Next, a manner of holding the first and second cylindrical lenses 6 and7 of the optical apparatus 1 will be described.

FIGS. 6A, 6B and 6C show an example of a holder for holding the firstcylindrical lens 6 and the second cylindrical lens 7 of the opticalapparatus 1. FIG. 6A is a cross-sectional view taken on a planeincluding the optical axis and parallel to the sub-scanning direction.FIG. 6B is a view projected on a plane seen from the light source side.FIG. 6C is a view projected on a plane which include the main scanningdirection and the optical axis. The the holder for holding the first andsecond cylindrical lenses 6 and 7 generally includes a base 18 attachedto the apparatus to support the entire holder, a first cylindrical lensholder 13 to which the first cylindrical lens 6 is attached, and asecond cylindrical lens holder 14 to which the second cylindrical lens 7is attached. The first cylindrical lens 6 and the second cylindricallens 7 (hatched in the figure) are rectangular lenses whose attachmentsurfaces are planes.

The base 18 substantially takes the shape of a rectangularparallelopiped on the upper surface of which is formed a V-groove 30extending in parallel with the optical axis. The second cylindrical lensholder 14 which substantially takes the shape of a cylinder is supportedby the V-groove 30 with its cylindrical surface in contact with theslanting surfaces of the V-groove 30. The V-groove 30 of the base 18 isformed so that the sub-scanning direction height of the generating lineof the second cylindrical lens 7 is aligned with the height of theoptical axis with the second cylindrical lens holder 14 supported in theV-groove.

The second cylindrical lens holder 14 substantially takes the shape of acylinder. More specifically, the second cylindrical lens holder 14includes two cylinders 14a and 14b and a connector 14c forming a part ofthe cylinders 14a and 14b to connect them along the generating line. Thecylinder 14a of the second cylindrical lens holder 14 is secured by aplate spring 19 so as not to move relative to the base 18. To an endsurface 14d of the other cylinder 14b of the second cylindrical lensholder 14 which is opposite the cylinder 14a, the second cylindricallens 7 is attached. The second cylindrical lens 7, which is made ofresin as mentioned above, is secured not by bonding but by being pressedby plate springs 15 and 16 screwed to the connector 14c. In the vicinityof the end surface 14d is formed a plane portion 14e which is inparallel with the main scanning surface. By setting the secondcylindrical lens 7 so that its attachment surface which is in parallelwith the cylinder generating line abuts the plane portion 14e, thesub-scanning direction heights of the cylinder generating line and theoptical axis are aligned. The inner diameter of the cylinder 14b of thesecond cylindrical lens holder 14 is the same as the outside diameter ofthe first cylindrical lens holder 13, and the first cylindrical lensholder 13 is partly inserted into the cylinder 14b. The firstcylindrical lens holder 13 is secured to the inner surface of thecylinder 14b by being pressed by a setting screw 17 inserted through theside wall of the cylinder 14b.

The first cylindrical lens holder 13 substantially takes shape of acylinder having in its center a hole for the light beam to passtherethrough. The side wall of the first cylindrical lens holder 13partly protrudes at the side which is not inserted into the secondcylindrical lens holder 14, and on the optical axis side surface of theprotruding portion is formed a plane portion 13a which is in parallelwith the main scanning surface. The first cylindrical lens 6 is bondedto the end surface which is not inserted into the second cylindricallens holder 14 and to the plane portion 13a. Similarly to the case ofthe plane portion 14e, by setting the first cylindrical lens 6 so thatits attachment surface which is in parallel with the cylinder generatingline abuts the plane portion 13a, the sub-scanning direction heights ofthe cylinder generating line and the optical axis are aligned.

The first cylindrical lens 6 and the second cylindrical lens 7 areadjusted in the following manner: First, the first cylindrical lens 6and the second cylindrical lens 7 are attached to the lens holders 13and 14, respectively. Then, the two lens holders 13 and 14 are engagedwith each other and the relative positions of the first and secondcylindrical lenses 6 and 7, i.e. the axial distance and the direction ofthe cylinder generating line are adjusted by rotating and moving theholders 13 and 14 until they are located in predetermined positions,respectively. Then, they are secured to form a lens block. On the otherhand, the base 18 is adjusted so that the central line of the V-groove30 is substantially aligned with the optical axis of the opticalapparatus, and is attached to the optical apparatus. The center of theoptical axis can be aligned only by placing the optically adjusted lensblock on the base 18. Lastly, the position of the lens block, i.e. theoptical axis direction distance from another optical element such as thelight source and the direction of the cylinder generating line areadjusted and the lens block is secured by the plane spring 19. Byadjusting in this manner, the cylindrical lenses can be easilypositioned.

FIGS. 7A to 7D show another example of the holder for holding the firstand second cylindrical lenses of the optical apparatus of theembodiments. FIG. 7A is a cross-sectional view taken on a planeincluding the optical axis and parallel to the sub-scanning direction.FIG. 7B is a view projected on a plane seen from the light source side.FIG. 7C is a cross-sectional view taken on a plane including the mainscanning direction and the optical axis. FIG. 7D is a view projected ona plane seen from the image side. In those figures, the holder forholding the first and second cylindrical lenses generally includes abase 18' attached to the apparatus to support the entire holder, a firstcylindrical lens holder 13 to which the first cylindrical lens 6 isattached, a second cylindrical lens holding member 20 to which thesecond cylindrical lens 7 is attached, and the second cylindrical lensholder 14'. The first cylindrical lens 6 and the second cylindrical lens7 (hatched in the figure) are rectangular lenses whose attachmentsurfaces are planes. The first cylindrical lens holder 13 has the samestructure as that of the holder of FIGS. 6A to 6C and descriptionthereof will not be given.

The base 18' substantially takes the shape of a plane. On the upperplane surface thereof, a positioning rail 18a' extending in parallelwith the optical axis is formed to protrude in the sub-scanningdirection. The optical axis side end surface of the positioning rail18a' is formed to be a plane vertical to the main scanning direction. Atan upper portion of the base 18', the second cylindrical lens holder 14'is mounted with its side surface pressed against the plane surface ofthe positioning rail 18a'.

The second cylindrical lens holder 14' includes a V-groove 14b'extending along the optical axis and a plane portion 14c' having an endsurface vertical to the optical axis. The second cylindrical lens holder14' is screwed to the base 18' through an elongate hole 14a' formed onthe central line of the bottom of the V-groove 14b' to be elongatedalong the optical axis. On the slanting surfaces of the V-groove 14b',the first cylindrical lens holder 13 is supported with its cylindricalside surface in contact with the slanting surfaces. The V-groove 14b' isformed so that the generating line of the first cylindrical lens 6attached to the first cylindrical lens holder 13 is located at apredetermined sub-scanning direction height. The first cylindrical lensholder 13' is secured so as not to move relative to the secondcylindrical lens holder 14' by a plane spring 19' screwed to the secondcylindrical lens holder 14'.

The second cylindrical lens holding member 20 takes the shape of aflange. The plane portion 14c' of the second cylindrical lens holder 14'has a through hole formed along the optical axis and the inner diameterof the through hole and the outer diameter of the thinner side of theflange-shaped second cylindrical lens holding member 20 are the same.The second cylindrical lens holding member 20 is screwed with itsthinner side inserted into the through hole of the second cylindricallens holder 14'. On the thicker side end surface of the secondcylindrical lens holding member 20, a plane portion 20a is formed inparallel with the main scanning direction to protrude along the opticalaxis for the positioning of the cylinder generating line of the secondcylindrical lens 7. The sub-scanning direction height of the secondcylindrical lens 7 is determined by setting the cylindrical lens 7 sothat its attachment surface which is parallel to the cylinder generatingline abuts the plane portion 20a. The second cylindrical lens 7 isattached to the holding member 20 by plane springs 15' and 16' screwedto the holding member 20.

In the holder of FIG. 7, the first and second cylindrical lenses 6 and 7are adjusted in the following manner: First, the first and secondcylindrical lenses 6 and 7 are secured to the first cylindrical lensholder 13' and to the second cylindrical lens holding member 20,respectively, and the second cylindrical lens holding member 20 isinserted into the through hole of the lens holder 14'. Then, the lensholder 13' is set so as to abut the V-groove 14b' of the lens holder 14,and the relative positions of the first and second cylindrical lenses 6and 7, i.e. the axial distance and the direction of the cylindergenerating line are adjusted by rotating and moving the lens holder 13until it is located in a predetermined position.

Then, the lens holder 13 is secured and the second cylindrical lensholding member 20 is screwed to the lens holder 14' to form a lensblock. The lens block is pressed against the positioning rail 18a' onthe base 18' to determine the main scanning direction central positionof the holder 14', and the position of the lens block, i.e. the opticalaxis direction distance from another optical element such as the lightsource and the direction of the cylinder generating line are adjusted.Then, the lens block is secured by a screw at the elongate hole 14a'. Byadjusting in this manner, the cylindrical lenses can be easilypositioned.

Next, conditions for the second cylindrical lens 7 and the image planeinclination correcting lens 12 in order that the spot diameter on thescanned surface does not vary even if the environmental temperaturevaries will be described in detail.

Referring to FIG. 5, there is schematically shown a sub-scanningdirection refractive power arrangement of the optical system of theembodiments of the present invention. In FIG. 5, f₁ is the focal lengthof the first cylindrical lens 6. f₂ is the focal length of the secondcylindrical lens 7. f₃ is the composite focal length of the firstscanning lens 9 and the second scanning lens 10. f₄ is the focal lengthof the image plane inclination correcting lens 12. The distance betweenthe rear principal point of the first cylindrical lens 6 and the frontprincipal point of the second cylindrical lens 7 is d. The distancebetween the image side principal point of the second cylindrical lens 7and the imaging point in the vicinity of the deflection surface is S.The distance between the image side principal point of the image planeinclination correcting lens 12 and the imaging point on the scannedsurface is L.

In the process of deriving the expressions shown below, it is assumedthat the variation in refractive index of the glass lenses and theeffect of thermal expansion of glass are sufficiently negligible for thevariation in configuration and refractive index of the secondcylindrical lens 7 and the image plane inclination correcting lens 12.

1. Basic Idea

For the self compensation of the imaging position by the secondcylindrical lens 7 and the image plane inclination correcting lens 12, avariation ΔL in the distance L due to a variation in refractive index ofthe second cylindrical lens 7 and a variation ΔL' in the distance L dueto a variation in refractive index of the image plane inclinationcorrecting lens 12 caused by a variation in temperature should equaleach other. That is, it is necessary that the following condition befulfilled:

    ΔL=-ΔL'                                        (1)

where ΔL is the variation in the distance L due to a variation inrefractive index of the second cylindrical lens 7, and ΔL' is thevariation in the distance L due to a variation in refractive index ofthe image plane inclination correcting lens 12.

ΔL and ΔL' can also be expressed as follows: ##EQU1## where T is thetemperature, and β₂ is the magnification of the second imaging portionin the sub-scanning direction. ##EQU2##

2. Derivation of ΔL

A specific manner of derivation of ΔL will be described.

The distance S between the image side principal point of the secondcylindrical lens 7 and the imaging point in the vicinity of thedeflection surface is expressed by the following expression (4):##EQU3##

The focal length f₂ of the second cylindrical lens 7 is expressed by thefollowing expression (5): ##EQU4##

The second cylindrical lens 7 is a plano-concave cylindrical lens planeto the light source side. When the radius of curvature of the concavesurface is r₂ and the refractive index thereof is n, the temperaturevariation is expressed by: ##EQU5## where a is a linear expansioncoefficient, n₀ is a design value of the refractive index, and dn/dT isa temperature coefficient of the refractive index.

From these expressions, the expression (5) is rearranged as: ##EQU6##

Thus, by substituting the expressions (4) and (6) into the expression(2), ΔL is obtained by the following expression (7): ##EQU7##

3. Derivation of ΔL'

A specific manner of derivation of ΔL' will be described below.

The distance L between the image side principal point of the image planeinclination correcting lens 12 to the imaging point on the scannedsurface is expressed by the following expression (8): ##EQU8##

The focal length f₄ of the image plane inclination correcting lens 12 isexpressed by the following expression (9): ##EQU9##

The image plane inclination correcting lens 12 is a planoconvexcylindrical lens convex to the light source side. When the radius ofcurvature of the convex surface is r₂ and the refractive index thereofis n, the temperature variation is expressed by: ##EQU10##

From these expressions, the expression (8) is rearranged as: ##EQU11##

Thus, by substituting the expressions (8) and (10) into the expression(3), ΔL' is obtained by the following expression (11): ##EQU12##

4. Self Temperature Compensation Condition

From the above, by substituting the expressions (7) and (11) into theexpression (1), the following expression (12) is obtained as a conditionfor the self temperature compensation of the imaging position by thesecond cylindrical lens 7 and the image plane inclination lens 12:##EQU13##

5. Modification of Self Temperature Compensation Condition

The self temperature compensation condition (12) is derived inconsideration of only the variation in refractive index of the secondcylindrical lens 7 and the image plane inclination correcting lens 12made of resin. In the actual scanning optical apparatus, however, thereare various other factors which affect the imaging condition of thelight beam. Therefore, it is difficult to make the temperaturecompensation only by the condition (12).

In particular, when the supporting member for the laser diode 2 and thecollimator lens 5 is made of a material which expands with an increasein temperature, the imaging position shifts in a direction to decreasethe distance L with an increase in temperature. The use of this actionfor the temperature compensation is effective since the focal length f₄can be reduced more than by the compensation only by use of thecondition (12).

The inventors of the present invention carried out various experimentsto find that, in consideration of the effect of variation in thedistance between the laser diode 2 and the collimator lens 5 for thecondition (12), it is preferred to modify the condition (12) to thecondition (13) shown below. It is assumed that the condition (13) covers0 or more (value of aluminum) as the linear expansion coefficient of thematerial of the supporting member for the laser diode 2 and thecollimator lens 5. ##EQU14##

When the lower limit of the condition (13) is exceeded, the imagingposition shifts excessively toward the light source side when thetemperature rises. When the upper limit is exceeded, the imagingposition shifts excessively toward the image side. These are bothundesirable.

Values of the expressions of the first to sixth embodiments are shown inTable 8.

                  TABLE 8                                                         ______________________________________                                        Values of Expressions of Embodiments                                                                                 Value of                                      f.sub.1                                                                            f.sub.2  d      f.sub.4                                                                             (13)                                        ______________________________________                                        1st      25.00  -10.00   16.25                                                                              90.02 -0.73                                                                              1.64                                 embodiment                                                                    2nd      30.00  -16.00   16.40                                                                              90.02 -0.73                                                                              1.72                                 embodiment                                                                    3rd      35.00  -25.00   14.38                                                                              90.02 -0.73                                                                              1.86                                 embodiment                                                                    4th      40.00  -35.00   12.00                                                                              90.02 -0.73                                                                              1.87                                 embodiment                                                                    5th      45.00  -45.00   10.13                                                                              90.02 -0.73                                                                              1.78                                 embodiment                                                                    6th      50.00  -60.00   5.00 90.02 -0.73                                                                              1.80                                 embodiment                                                                    ______________________________________                                    

Note: d is calculated by the following expression: ##EQU15## where f(composite focal length of f₁ and f₂)=200.

In the first to sixth embodiments, since the condition (13) isfulfilled, even if the refractive power of the image plane inclinationcorrecting lens 12 having a positive refractive power varies due to anincrease in the environmental temperature, the imaging position on thescanned surface does not vary since the refractive power of the secondcylindrical lens 7 having a negative refractive power and the distancebetween the laser diode 2 and the collimator lens 5 compensate for therefractive power of the image plane inclination correcting lens 12.

As described above, the scanning optical apparatus according to thepresent invention has a high capability of correcting the image planeinclination error of the deflection surface and even if theenvironmental temperature varies, the first lens having a negativerefractive power and made of resin and the second lens having a positiverefractive power and made of resin act to compensate for each other'srefractive powers, so that the imaging position on the scanned surfacedoes not vary.

Therefore, when employed in an image forming apparatus such as a printerand a digital copying machine, since the imaging position is compensatedfor when the environmental temperature varies, it proves to be an imageforming apparatus of a high image quality.

Since the lens arrangement of the first imaging portion enables areduction in the total length of the first imaging portion while thesub-scanning direction magnification of the second imaging portion isreduced, a compact optical apparatus is realized.

In addition, in this scanning optical apparatus, since there is noresin-made lens having refractive power in the main scanning direction,a stable imaging condition is maintained in the main scanning direction.

In the lens holder of this scanning optical apparatus, since the twolenses having different refractive powers in the main and sub-scanningdirections can be accurately positioned, the spot on the scanned surfaceis formed with an excellent position accuracy, so that the quality ofthe image formed by the scanning optical apparatus using the lens holderimproves.

FIGS. 8 to 16 show a second implementation of the present invention.Hereinafter, embodiments of a scanning optical apparatus of the secondimplementation will be described.

FIGS. 8A and 8B show the refractive power arrangement and optical pathof the laser scanning optical system of the present invention. FIG. 8Ashows the cross section in the main scanning direction. FIG. 8B showsthe cross section in the sub-scanning direction. Reference numeral 201represents a light source. Reference numeral 202 represents an objectivelens. Reference numeral 203 represents an anamorphic lens which forms afirst imaging portion G1. Reference designation 203a represents a glasslens (hereinafter, sometimes referred to as "first cylindrical lens",but not necessarily a cylindrical lens) having a positive refractivepower in the sub-scanning direction. Reference designation 203brepresents a resin lens (hereinafter, sometimes referred to as "secondcylindrical lens", but not necessarily a cylindrical lens) having anegative refractive power in the sub-scanning direction. Referencenumeral 204 represents a deflective reflection surface. Referencenumeral 205 represents a scanning lens which forms a second imagingportion G2. Reference numeral 206 represents a scanned surface (imageplane). Reference designation H represents the principal point of theanamorphic lens 203 (first and second cylindrical lenses 203a and 203b).

The lens elements included in the scanning lens 205 are all made ofresin, and as shown in FIG. 8A, the overall refractive power of thescanning lens 205 is substantially null in the main scanning direction.Now, the reason will be described why this arrangement is advantageousin preventing an image plane shift due to a variation in temperature atthe cross section in the main scanning direction.

When the scanning lens is an fθ lens, from a relationship y'=fθ, thefocal length f of the fθ lens is univocally determined to be a positivevalue from the angle of scanning and the angle of view. For example, inthe case of an fθ lens for A3 size (the shorter side is 297 mm), thefocal length f with the half angle of view θ as the parameter is asshown in Table 9.

                  TABLE 9                                                         ______________________________________                                        Half angle of view                                                                         15     20     25   30   35   40   45                             (deg)                                                                         Focal length (mm)                                                                         567    425    340  284  243  213  189                             ______________________________________                                    

The scanning lens must be overall positive even if it includes aplurality of lens elements. Therefore, when the scanning lens includes asingle lens having a negative refractive power, a positive lens suchthat the absolute value of its refractive power is greater than that ofthe refractive power of the negative lens should be included in thescanning lens.

With respect to the single lens, a relationship among the refractiveindex, the radii of curvature of the surfaces and the focal length willbe examined. The focal length of the single lens is represented by thefollowing expression (14): ##EQU16## where f is the focal length of thesingle lens, n is the refractive index of the single lens, r1 is theradius of curvature of the light source side surface, and r2 is theradius of curvature of the image plane side surface.

In order to simplify the expression (14), a case will be consideredwhere the positive lens is a plano-convex lens (f>0) and the negativelens is a plano-concave lens (f<0). When r is the radius of curvature ofthe spherical surfaces of each of the lenses, the focal length of theplano-convex lens is f=r/(n-1) and the focal length of the plano-concavelens is f=-r/(n-1). In either case, the absolute value |f| of the focallength increases with an increase in the radius of curvature r of thespherical surface and decreases with an increase in the refractive indexn. Therefore, the absolute value of the refractive power increases witha decrease in the radius of curvature r of the spherical surface andincreases with an increase in the refractive index n.

On the other hand, the variation in refractive index and in linearexpansion according to the temperature differ between glass and resin.Table 10 shows a variation in refractive index dn/dT and a linearexpansion coefficient (1/1)·(d1/dT) with respect to BK7 and AC which areexamples of glass and resin, respectively. It is understood from Table10 that resin is greater than glass in the linear expansion coefficientby one digit and in the variation in refractive index by two digits.

                  TABLE 10                                                        ______________________________________                                        Lens material                                                                                 ##STR1##                                                                                ##STR2##                                            ______________________________________                                        BK7 (Glass)    7.8 × 10.sup.-6                                                                    2.6 × 10.sup.-6                               AC (Resin)     7.0 × 10.sup.-5                                                                   -1.07 × 10.sup.-4                              ______________________________________                                    

When the temperature varies, in glass, the variation in the radius ofcurvature r and the variation in the refractive index n compensate forthe variation in the focal length f, whereas in resin, the variation inthe radius of curvature r and the variation in the refractive index nmultiply the variation in the focal length f. Therefore, comparing aglass lens and a resin lens having the same focal length f, thevariation in the focal length f due to a variation in temperature isgreater in the resin lens by far than in the glass lens.

Next, a relationship will be described between the absolute value of therefractive power and a variation in a back focal length Bf at the crosssection in the main scanning direction when the lens elements includedin the scanning lens are all made of resin. When the scanning lens is anfθ lens, the focal length f is represented by an expression (15) shownbelow. As is understood from the expression (15), if a width of scanningW and the half angle of view θ are determined, the focal length f of thefθ lens is univocally determined. That is, when the width of scanning Wis constant, the greater the half angle of view θ is, the shorter thefocal length f is (i.e. the greater the refractive power is). ##EQU17##where W is the width of scanning, θ is the half angle of view (deg), andf is the focal length.

When the scanning lens 205' is an fθ lens as shown in FIG. 9A, since thefθ lens has a strong positive refractive power, if the refractive powervaries due to a variation in temperature, the back focal length Bfvaries accordingly. As described above, the greater the absolute valueof the refractive power is, the more readily the back focal length Bf isaffected by a variation in temperature. However, if the focal length fis increased in order to reduce the variation in the back focal lengthBf due to a variation in temperature, the distance from the deflectivereflection surface to the scanned surface (i.e. the total length of thelaser scanning optical system) will increase. Thus, it is inadvisable toincrease the focal length f.

In a laser scanning optical system of a type in which converged light isincident on the scanning lens at the cross section in the main scanningdirection, the refractive power of the scanning lens can be reducedwithout reference to the expression (15). Therefore, as shown in FIG.9B, if a scanning lens 205 having a null refractive power in the mainscanning direction is used, the variation in refractive power caused bya variation in temperature is extremely small since the refractive poweris null. As a result, the variation in the back focal length Bf due to avariation in temperature is extremely small. Therefore, qualitatively,the greater the absolute value of the refractive power of the scanninglens is, the greater the variation in the back focal length Bf due to avariation in temperature is.

Next, a variation in the back focal length Bf due to a variation intemperature when the scanning lens includes a plurality of positive andnegative resin lens elements at the cross section in the main scanningdirection will be described. In an arrangement where the scanning lens205 includes from the light source side a negative lens element 205a anda positive lens element 205b as shown in FIG. 9C, when the temperaturerises, the absolute values of refractive powers of the lens elements205a and 205b both decrease, so that the negative lens element 205a actson the back focal length Bf so that the image plane returns toward theminus side and the positive lens element 205b acts so that the imageplane retreats toward the plus side. Therefore, when the overallrefractive power is positive like the fθ lens, the effect of retreatingthe image plane toward the plus side when the temperature risesincreases and becomes dominant.

When positive and negative resin lens elements such that the absolutevalues of their refractive powers are close to each other are combined,the effect of returning the image plane toward the minus side by thenegative lens element and the effect of retreating the image planetoward the plus side by the positive lens element are in equilibrium andcompensate for each other. Therefore, in a scanning lens including aplurality of positive and negative resin lens elements at the crosssection in the main scanning direction and the overall refractive powerof which is substantially null in the main scanning direction, thevariation in the back focal length Bf is minimized, so that the imageshift due to a variation in temperature is prevented with respect to themain scanning direction.

Thus, since the lens elements included in the scanning lens of thepresent invention (corresponding to the second image forming opticalsystem of Japanese Published Patent Application H4-47803) are all madeof resin and the overall refractive power of the scanning lens issubstantially zero at the cross section in the main scanning direction,the variation in focal length due to a variation in temperature does notoccur in theory at the cross section in the main scanning direction, sothat the position of the image plane hardly varies.

The refractive power φ which is substantially null is less than half therefractive power (=1/f) of the fθ lens. That is, it can be said that arefractive power is substantially null if the following condition (16)or (17) is fulfilled: ##EQU18##

In the case of a scanning lens of subsequently shown embodiment andexample for comparison, ##EQU19## Therefore, the condition (17) isfulfilled.

Next, the temperature compensation in the sub-scanning direction will bedescribed. As described previously, with respect to the cross section inthe main scanning direction, since the overall refractive power of theresin-made scanning lens is null, the variation in back focal length dueto a variation in temperature does not occur. With respect to the crosssection in the sub-scanning direction, however, since the resin-madescanning lens has a strong positive power, the image plane shiftsrearward (toward the plus side in FIG. 9C) as the temperature rises.

To solve this problem, in the present invention, the anamorphic lenshaving refractive power only at the cross section in the sub-scanningdirection is formed of a negative resin lens element and a positiveglass lens element so that the overall power is positive. With thisarrangement, for example, the retreat of the image plane caused by thescanning lens when the temperature rises is canceled by the return ofthe image plane caused by the negative resin lens.

This will be described with reference to FIG. 10B. FIG. 10B shows thestructure of the laser scanning optical system of the present inventionat the cross section in the sub-scanning direction. FIG. 10A shows ageneral laser scanning optical system having the same total length asthe laser scanning optical system of Fig. 10B (but having no temperaturecompensating function). First, with respect to the second cylindricallens 203b FIG. 10B, when the temperature rises with the luminous fluximaged on the deflective reflecting surface 204, the absolute value ofnegative refractive power of the resin-made second cylindrical lens 203bdecreases. For this reason, the imaging position shifts toward the sideof the light source 201 by a distance d. The shift of the imagingposition causes the image plane on the scanned surface 206 to shifttoward the side of the light source 201 by the distance D. However, theabsolute value of refractive power of the scanning lens 205 decreasesdue to the temperature rise as well as the refractive power of thesecond cylindrical lens 203b varies. For this reason, the shift of theimage plane by the distance D is canceled and the position of the imageplane is maintained on the scanned surface 206. Specifically, thevariation in refractive power of the negative resin lens 203b whichreturns the image plane 206 toward the side of the light source 201counteracts the variation in refractive power of the positive scanninglens 205 which retreats the image plane 206, whereby the shift of theimage plane in the sub-scanning direction due to a variation intemperature is compensated for.

Next, a preferred lens arrangement and lens configuration of theanamorphic lens at the cross section in the sub-scanning direction willbe described with reference to FIG. 11. FIG. 11 shows how the luminousflux having exited from the objective lens is imaged on the deflectivereflection surface 204 by the anamorphic lens at the cross section inthe sub-scanning direction. When the refractive power of the lenselement disposed on the light source side is φ₁ and the refractive powerof the lens element disposed on the side of the deflective reflectionsurface 204 is φ₂ and the overall refractive power is φ, in ananamorphic lens of a positive, negative configuration from the lightsource side (0<φ₁, φ₂ <0) as shown in FIG. 11A, φ=φ₁ +φ₂ -e·φ₁ ·φ₂. Inan anamorphic lens of a negative, positive configuration from the lightsource side (φ₁ <0, 0<φ₂) as shown in FIG. 11B, φ'=φ₁ '+φ₂ '-e'·φ₁ '·φ₂'.

The image plane inclination correcting anamorphic lens 203 of thepresent invention may be of a positive, negative configuration from thelight source side (FIG. 11A) or may be of a negative, positiveconfiguration (FIG. 11B). However, the positive, negative configurationfrom the light source side is preferred. The reason therefor will bedescribed in the following:

The Japanese Published Patent Application H4-47803 describes thatdisposing a negative cylindrical lens on the side of the light source201 is advantageous in practical use since a long distance is securedbefore the line image. However, it cannot be advantageous in practicaluse that the anamorphic lens 203 which forms a line image is positionedaway from the deflector. This is because the arrangement of the numberof apertures (NA) in the entire optical system from the light source tothe scanned surface at the cross sections in the main and sub-scanningdirections is ignored and only the paraxial refractive power arrangementis considered. For example, although it is necessary to consider thelength-to-width ratio of the radiation angle characteristic of asemiconductor laser serving as the light source and the magnification ofthe scanning lens at the cross section in the sub-scanning direction, ifthese are actually considered, the NA becomes too dark at the crosssection in the sub-scanning direction, so that no optical system can beformed unless most of the luminous flux is cut off at an aperture or thecylindrical lens is disposed considerably away from the deflector. Inview of any aspect such as the size reduction of the laser scanningoptical system, the brightness of the NA at the cross section in thesub-scanning direction and the mechanical strength of the light sourceportion in realizing a multi-beam light source, it is advantageous thatthe distance from the cylindrical lens to the deflector is short.

The magnification of the scanning lens which maintains the deflectivereflection surface and the scanned surface in a conjugate relationshipat the cross section in the sub-scanning direction is normally 3× to 4×.If the magnification is as low as 1×, the focal length of the anamorphiclens increases, so that the distance from the light source to thedeflective reflection surface increases. However, if the anamorphic lensis of the positive, negative configuration from the light source side(FIG. 11A), the principal point H shifts frontward (toward the lightsource side), so that the distance from where the lens is actuallypositioned to the deflective reflection surface 4 is shorter than thefocal length. Therefore, disposing the positive glass lens element onthe light source side and the negative resin lens element on thedeflector side is more effective in reducing the optical path andenables the image plane inclination correction at a low magnificationand the size reduction of the laser scanning optical system.

On the other hand, when the anamorphic lens is of the negative, positiveconfiguration from the light source side as shown in Japanese PublishedPatent Application H4-47803, since the principal point H shifts rearward(toward the deflective surface side), the distance from where thecylindrical lens is positioned to the deflective reflection surface 204is longer than the actual focal length.

In either of the above-described cases, the positive glass lens elementmay be a bi-convex lens, a plano-convex lens or a meniscus lens.Likewise, the negative resin lens element may be a bi-concave lens, aplano-concave lens or a meniscus lens.

The image plane inclination correcting anamorphic lens may be formed ofa combination of single lenses such as a combination of a positiveplano-convex lens and a negative plano-concave lens or a combination ofa positive bi-convex lens and a negative bi-concave lens such that theradius of curvature is the same on the both side surfaces. Moreover, theanamorphic lens may be formed of a combination of lenses havingdifferent radii of curvature, respectively, so that aberration of thescanning lens is corrected at the cross section in the sub-scanningdirection. This arrangement is advantageous, particularly, for use in alaser scanning optical system which supports high print density, and issuitable for use in a laser beam printer with a high record density.

According to such features, since the overall refractive power of thescanning lens is substantially null in the main scanning direction, theimage plane does not shift at the cross section in the main scanningdirection even if the temperature varies. On the other hand, at thecross section in the sub-scanning direction, the image plane shiftcaused by a variation in the temperature of the scanning lens iscompensated for by the image plane shift caused by a variation in thetemperature of the negative resin lens included in the image planeinclination correcting anamorphic lens. In addition, since the positiveglass lens included in the anamorphic lens is hardly affected by avariation in temperature, a variation in its temperature does not affectthe position of the image plane.

Hereinafter, an embodiment of the laser scanning optical systemaccording to the second implementation of the present invention and anexample for comparison with the embodiment will be described. First,numerical data of the embodiment (temperature compensation is made) andthe example for comparison (temperature compensation is not made) areshown with respect to before and after a variation in temperature. Inthe embodiment and the example for comparison, Si (i=1,2,3, . . . )represents an ith surface counted from the laser source side, ri(i=1,2,3, . . . ) represents the radius of curvature, in the mainscanning direction, of an ith surface counted from the laser source side(with respect to rotationally symmetrical surfaces, the radius ofcurvature in the sub-scanning direction is also shown), di (i=1,2,3, . .. ) represents the axial distance between an ith surface and an i+1thsurface counted from the laser source side, and Ni (i=1,2,3, . . . )represents the refractive index, to light of a wavelength of 780 nm, ofan ith lens counted from the laser source side. f₁ represents the focallength of the first cylindrical lens 203a. f₂ is the focal length of thesecond cylindrical lens 203b. f_(A) is the focal length of the imageplane inclination correcting anamorphic lens 203 or 203' (in the case ofthe embodiment, the composite focal length of the first and secondcylindrical lenses 203a and 203b).

In the embodiment and the example for comparison, the deflectivereflection surface 204 side surface of a fourth scanning lens g4included in the scanning lens 205 is a toric surface having differentrefractive powers in the main and sub-scanning directions. Taking adeformed toric surface as an example, a Z toric surface of the fourthscanning lens g4 will be described. This surface is a toric surface suchthat its main scanning direction cross section is aspherical and theradius of curvature in the sub-scanning direction continuously changesalong the main scanning direction cross section. This surface is definedas a function of y and z by the following expression (A): ##EQU20##

That is, the deformed Z toric surface is obtained as a reference z toricsurface to which a two-dimensional additive term A(y,z) is added. Here,when a main curve is a curve at the cross section in the main scanningdirection and a profile curve is a curve at the cross section in thesub-scanning direction (i.e. x direction is the direction along theoptical axis, y direction is the main scanning direction, and zdirection is the sub-scanning direction), K and c are curvatures(exactly, K+2a₀,2 and c+2a₂,0, respectively) at the vertices along themain and profile curves, respectively (i.e. 1/K is the radius ofcurvature at the vertex along the main curve and 1/c is the radius ofcurvature along the profile curve (radius of curvature in thesub-scanning direction at the vertex of the main curve)), and μ and.di-elect cons. are conic constants (hyperbola when negative, parabolawhen zero, ellipse when positive, circle when 1) along the main andprofile curves, respectively.

For example, when μ=1 and A=0, the expression (A) represents aconventional toric surface (secondary profile curve ρ rotated with aradius of 1/K about an axis parallel to the Z axis). A of the expression(A) is expressed by the following expression: ##EQU21## where a₀,0.tbd.0, a_(i),1 .tbd.0, and a₁,j .tbd.0.

In each table (Tables 10 to 13), the surfaces marked with asterisks arerotationally symmetrical aspherical surfaces and defined by thefollowing expression representing the surface configuration of anaspherical surface: ##EQU22## where X is a displacement amount along theoptical axis from a reference surface, Y is a height in a directionvertical to the optical axis, C is a paraxial curvature, .di-elect cons.is a conic constant, and Ai is an ith aspherical coefficient(i=4,6,8,10).

Data obtained from the present implementation before temperaturevariation (temperature: 20° C.) are listed in Table 11.

Data obtained from the present implementation after temperaturevariation (temperature: 40°) are listed in Table 12.

Data obtained from an example for comparison before temperaturevariation (temperature: 20° C.) are listed in Table 13.

Data obtained from an example for comparison after temperature variation(temperature: 40° C.) are listed on Table 14.

                  TABLE 11                                                        ______________________________________                                              Radius of                                                                     Curvature in                                                                  Main Scanning                                                                              Axial       Refractive                                     Surface                                                                             Direction    Distance    Index                                          ______________________________________                                         Image plane inclination correcting anamorphic lens 203:                      f.sub.A = 150!                                                                (1st cylindrical lens 203a, made of glass: f1 = 14)                           S1    r1         ∞ (Radius of curvature in                                               sub-scanning direction: 7.1564)                                                 d1 2.000    N1 1.51118                                     S2    r2 ∞   d2 2.95108                                                 (2nd cylindrical lens 203b, made of resin: f.sub.2 = 31 10)                   S3    r3 ∞   d3 1.0000   N2 1.51882                                     S4    r4 ∞   (Radius of curvature in                                                       sub-scanning direction: 5.1883)                                               d4 64.420                                                   Deflective reflection surface 204!                                           S5    r5 ∞   d5 35.000                                                   Scanning lens 205!                                                           (1st scanning lens g1)                                                        S6    r6 ∞   d4 4.000    N2 1.51882                                     S7    r7 243.76391 d5 32.000                                                  (2nd scanning lens g2)                                                        S8    r8 -1070.40022                                                                             d6 8.000    N3 1.51882                                     S9    r9 -201.24004                                                                              d7 37.000                                                  (3rd scanning lens g3)                                                        S10*  r10 297.19625                                                                              d8 8.000    N4 1.51882                                     S11*  r11 559.69732                                                                              d9 70.000                                                  (4th scanning lens g4)                                                        S12   r12 ∞  (Radius of curvature in                                                       sub-scanning direction: 49.20499)                                             d10 5.000   N5 1.51882                                     S13   r13 ∞  d11 168.855                                                 Scanned surf ace 206!                                                        S14   r14 ∞                                                             Aspherical Data of                                                            Rotationally Symmetrical Aspherical Surfaces                                  S10:  ε =                                                                             1.0000                                                              A4 =     -0.14046825 × 10.sup.-6                                        A6 =      0.58736024 × 10.sup.-12                                       A8 =      0.15081803 × 10.sup.-15                                       A10 =    -0.23871994 × 10.sup.-20                                 S11:  ε =                                                                            1.0000                                                               A4 =     -0.16365933 × 10.sup.-6                                        A6 =      0.23075207 × 10.sup.-12                                       A8 =     -0.14396003 × 10.sup.-15                                       A10 =     0.11999272 × 10.sup.-19                                 Aspherical Data of                                                            Rotationally Asymmetrical Aspherical Surface                                  S12:  Z toric surface                                                         ε =                                                                              1.0000                                                             1/c =      49.20499                                                           p =        1.0000                                                             1/K =      ∞                                                            a.sub.2,2 =                                                                              -0.23 × 10.sup.-6                                            a.sub.2,4 =                                                                              0.61 × 10.sup.-11                                            ______________________________________                                    

                  TABLE 12                                                        ______________________________________                                              Radius of                                                                     Curvature in                                                                  Main Scanning                                                                              Axial       Refractive                                     Surface                                                                             Direction    Distance    Index                                          ______________________________________                                         Image plane inclination correcting anamorphic lens 203:                      f.sub.A = 150!                                                                (1st cylindrical lens 203a, made of glass: f1 = 14)                           S1    r1         ∞ (Radius of curvature in                                               sub-scanning direction: 7.1564)                                                 d1 2.000    N1 1.51123                                     S2    r2 ∞   d2 2.95108                                                 (2nd cylindrical lens 203b, made of resin: f.sub.2 = 31 10)                   S3    r3 ∞   d3 1.0000   N2 1.51668                                     S4    r4 ∞   (Radius of curvature in                                                       sub-scanning direction: 5.1883)                                               d4 64.420                                                   Deflective reflection surface 204!                                           S5    r5 ∞   d5 35.000                                                   Scanning lens 205!                                                           (1st scanning lens gl)                                                        S6    r6 ∞   d4 4.000    N2 1.51668                                     S7    r7 244.10518 d5 32.000                                                  (2nd scanning lens g2)                                                        S8    r8 -1071.89878                                                                             d6 8.000    N3 1.51668                                     S9    r9 -201.52178                                                                              d7 37.000                                                  (3rd scanning lens g3)                                                        S10*  r10 297.61233                                                                              d8 8.000    N4 1.51668                                     S11*  r11 559.69732                                                                              d9 70.000                                                  (4th scanning lens g4)                                                        S12   r12 ∞  (Radius of curvature in                                                       sub-scanning direction: 49.27388)                                             d10 5.000   N5 1.51668                                     S13   r13 ∞  d11 168.855                                                 Scanned surf ace 206!                                                        S14   r14 ∞                                                             Aspherical Data of                                                            Rotationally Symmetrical Aspherical Surfaces                                  S10:  ε =                                                                             1.0000                                                              A4 =     -0.13987993 × 10.sup.-6                                        A6 =      0.58326593 × 10.sup.-12                                       A8 =      0.14934826 × 10.sup.-15                                       A10 =    -0.23573302 × 10.sup.-20                                 S11:  ε =                                                                            1.0000                                                               A4 =     -0.16297388 × 10.sup.-6                                        A6 =      0.22914357 × 10.sup.-12                                       A8 =     -0.14255709 × 10.sup.-15                                       A10 =     0.11849134 × 10.sup.-19                                 Aspherical Data of                                                            Rotationally Asymmetrical Aspherical Surface                                  S12:  Z toric surface                                                         ε =                                                                              1.0000                                                             1/c =      49.27388                                                           p =        1.0000                                                             1/K =      ∞                                                            a.sub.2,2 =                                                                              -0.23 × 10.sup.-6                                            a.sub.2,4 =                                                                              0.61 × 10.sup.-11                                            ______________________________________                                    

                  TABLE 13                                                        ______________________________________                                              Radius of                                                                     Curvature in                                                                  Main Scanning                                                                              Axial       Refractive                                     Surface                                                                             Direction    Distance    Index                                          ______________________________________                                        Image plane inclination correcting anamorphic lens 203                        cylindrical lens), made of glass: f.sub.A = 150                               S1    r1 ∞   (Radius curvature in                                                          b-scanning direction: 76.6772)                                                d1 5.000    N1 1.51118                                     S2    r2 ∞   d2 112.5                                                    Deflective reflection surface, 204!                                          S3    r3 ∞   d3 35.000                                                   Scanning lens 205!                                                           (1st scanning lens g1)                                                        S4    r4 ∞   d4 4.000    N2 1.51882                                     S5    r5 243.76391 d5 32.000                                                  (2nd scanning lens g2)                                                        S6    r6 -1070.40022                                                                             d6 8.000    N3 1.51882                                     S7    r7 -201.24004                                                                              d7 37.000                                                  (3rd scanning lens g3)                                                        S8*   r8 297.19625 d8 8.000    N4 1.51882                                     S9*   r9 559.69732 d9 70.000                                                  (4th canning lens g4).                                                        S10   r10 ∞  (Radius of curvature in                                                       sub-scanning direction: 49.20499)                                             d10 5.000   N5 1.51882                                     S11   r11 ∞  d11 168.855                                                 Scanned surface 206!                                                         S12   r12 ∞                                                             Aspherical Data of                                                            Rotationally Symmetrical Aspherical Surfaces                                  S8:    δ =                                                                             1.000                                                                 A4 =    -0.14046825 × 10.sup.-6                                         A6 =    0.58736024 × 10.sup.-12                                         A8 =    0.15081803 × 10.sup.-15                                         A10 =   -0.23871994 × 10.sup.-20                                 S9:    δ =                                                                             1.0000                                                                A4 =    -0.16365933 × 10.sup.-6                                         A6 =    0.23075207 × 10.sup.-12                                         A8 =    -0.14396003 × 10.sup.-15                                        A10 =   0.11999272 × 10.sup.-19                                  Aspherical Data of                                                            Rotationally Asymmetrical As#herica1 Surface                                  S10:  Z toric surface                                                         δ =  1.000                                                              1/c =      49.20499                                                           p =        1.0000                                                             1/K =      ∞                                                            a.sub.2,2 =                                                                              -0.23 × 10.sup.-6                                            a.sub.2,4 =                                                                              0.61 × 10.sup.-11                                            ______________________________________                                    

                  TABLE 14                                                        ______________________________________                                              Radius of                                                                     Curvature in                                                                  Main Scanning                                                                              Axial       Refractive                                     Surface                                                                             Direction    Distance    Index                                          ______________________________________                                        Image plane inclination correcting anamorphic lens 203'                       cylindrical lens), made of glass: f.sub.A = 150                               S1    r1 ∞   (Radius curvature in                                                          b-scanning direction: 76.6772)                                                d1 5.000    N1 1.51123                                     S2    r2 ∞   d2 112.5                                                    Deflective reflection surface, 204!                                          S3    r3 ∞   d3 35.000                                                   Scanning lens 205!                                                           (1st scanning lens g1)                                                        S4    r4 ∞   d4 4.000    N2 1.51668                                     S5    r5 243.76391 d5 32.000                                                  (2nd scanning lens g2)                                                        S6    r6 -1071.89878                                                                             d6 8.000    N3 1.51668                                     S7    r7 -201.24004                                                                              d7 37.000                                                  (3rd scanning lens g3)                                                        S8*   r8 -201.52178                                                                              d8 8.000    N4 1.51668                                     S9*   r9 559.69732 d9 70.000                                                  (4th canning lens g4)                                                         S10   r10 ∞  (Radius of curvature in                                                       sub-scanning direction: 49.27388)                                             d10 5.000   N5 1.51668                                     S11   r11 ∞  d11 168.855                                                 Scanned surface 206!                                                         S12   r12 ∞                                                             Aspherical Data of                                                            Rotationally Symmetrical Aspherical Surfaces                                  S8:    δ =                                                                             1.000                                                                 A4 =    -0.13987993 × 10.sup.-6                                         A6 =    0.58326593 × 10.sup.-12                                         A8 =    0.14934826 × 10.sup.-15                                         A10 =   -0.23573302 × 10.sup.-20                                 S9:    δ =                                                                             1.0000                                                                A4 =    -0.16297388 × 10.sup.-6                                         A6 =    0.22914357 × 10.sup.-12                                         A8 =    -0.14255709 × 10.sup.-15                                        A10 =   0.11849134 × 10.sup.-19                                  Aspherical Data of                                                            Rotationally Asymmetrical Aspherical Surface                                  S10:  Z toric surface                                                         δ =  1.000                                                              1/c =      49.27388                                                           p =        1.0000                                                             1/K =      ∞                                                            a.sub.2,2 =                                                                              -0.23 × 10.sup.-6                                            a.sub.2,4 =                                                                              0.61 × 10.sup.-11                                            ______________________________________                                    

FIG. 12 cross-sectionally shows the lens arrangement and optical pathfrom the deflective reflection surface 204 to the scanned surface 206 ofthe embodiment and the example for comparison with respect the mainscanning direction. Reference designation K at the optical pathrepresents a beam with an angle of view (angle of deflection) θ andexpressed by K=S1 (distance from the deflective reflection surface tothe object surface)×sinθ. FIG. 13 cross-sectionally shows the lensarrangement and optical path from the anamorphic lens 203 to the scannedsurface 206 in the embodiment with respect to the sub-scanningdirection. FIG. 14 cross-sectionally shows the lens arrangement andoptical path from the anamorphic lens 203 to the deflective reflectionsurface 204 in the embodiment with respect to the sub-scanningdirection. FIG. 15 cross-sectionally shows the lens arrangement andoptical path from the anamorphic lens 203' to the scanned surface 206 inthe example for comparison with respect to the sub-scanning direction.FIG. 16 cross-sectionally shows the lens arrangement and optical pathfrom the anamorphic lens 203' to the deflective reflection surface 204in the example for comparison with respect to the sub-scanningdirection.

In the data of the embodiment and the example for comparison, thescanning lens 205 is common and the first to third scanning lenses g1 tog3 thereof include rotationally symmetrical surfaces (therefore, theradii of curvature in the main and sub-scanning directions are thesame). The focal length of the single glass-made cylindrical lens 203'used in the example for comparison is 150 mm. Likewise, the compositefocal length of the first cylindrical lens 203a having a positiverefractive power and made of glass and the second cylindrical lens 203bhaving a negative refractive power and made of resin used in theembodiment is set to be 150 mm.

If the combination of focal lengths of the first and second cylindricallenses 203a and 203b having positive and negative refractive powers,respectively, is changed, the degree of effect of the temperaturevariation on the variation in the back focal length of the negative,resin-made second cylindrical lens 203b is changed, so that thecondition for the temperature compensation is not fulfilled. However,the combination of focal lengths of the positive (glass) and negative(resin) first and second cylindrical lenses 203a and 203b fulfilling thecondition for the temperature compensation exists continuously andinnumerably. That is, in a graph with the longitudinal axis representingthe focal length f₁ and the lateral axis representing the focal lengthf₂, a continuous curve is obtained by plotting the points fulfilling thecondition for the temperature compensation.

The variation in the back focal length Bf at the main and sub-scanningdirection cross sections before and after a temperature variation in theexample for comparison and in the embodiment is summarized as shown inTables 14 and 15.

                  TABLE 14                                                        ______________________________________                                        Embodiment (Temperature Compensation Is Made)                                 Anamorphic Lens Includes                                                      positive Glass Lens and Negative Resin Lens                                          20° C.                                                                             40° C.                                                     (Before variation)                                                                        (After variation)                                                                         Variation                                      ______________________________________                                        Main     0.0046        0.2185      0.2139                                     scanning                                                                      direction                                                                     Sub      0.3976        0.4955      0.0979                                     scanning                                                                      direction                                                                     ______________________________________                                    

                  TABLE 15                                                        ______________________________________                                        Example for Comparison (Temperature Compensation Is Not Made)                 Anamorphic Lens Includes One positive Glass Lens                                     20° C.                                                                             40° C.                                                     (Before variation)                                                                        (After variation)                                                                         Variation                                      ______________________________________                                        Main     0.0001        0.2147      0.2146                                     scanning                                                                      direction                                                                     Sub      0.4729        2.3029      1.8300                                     scanning                                                                      direction                                                                     ______________________________________                                    

With respect to the main scanning direction, since the refractive poweris null both in the embodiment and the example for comparison asdescribed above, the variation is as small as approximately 0.21 mm.With respect to the sub-scanning direction, while the variation is asgreat as 1.83 mm in the example for comparison, the variation is assmall as 0.0979 mm in the embodiment. Thus, it should be understood thatthe temperature compensation is effectively made in the embodiment.

What is claimed is:
 1. A scanning optical apparatus, comprising:a lightsource; a deflector for deflecting a light beam emitted from the lightsource to a main scanning direction; a first imaging unit, including afirst resin lens having a negative refractive power only in asub-scanning direction perpendicular to the main scanning direction, formaking the light beam emitted from the light source form an image in thevicinity of the deflection position of said deflector in thesub-scanning direction; and a second imaging unit, including a secondresin lens having a positive refractive power only in the sub-scanningdirection, for making the light beam deflected by the deflector form animage on a scanned surface in the sub-scanning direction wherein saidfirst resin lens and said second resin lens compensate for variation ineach other's refractive power due to temperature changes.
 2. A scanningoptical apparatus as claimed in claim 1, wherein said first imaging unitincludes, from the light source, a glass lens having a positiverefractive power only in the sub-scanning direction and said first resinlens.
 3. A scanning optical apparatus as claimed in claim 1, whereinsaid second imaging unit includes, from the light source, a glass lenshaving a negative refraction power, a glass lens having a positiverefractive power and said second resin lens.
 4. A scanning opticalapparatus as claimed in claim 1, wherein a collimated light beam isincident on said deflector.
 5. A scanning optical apparatus,comprising:a light source; an objective lens unit for condensing a lightbeam emitted from said light source; a first imaging unit for convergingthe light beam having passed through said objective lens unit in asub-scanning direction; a deflector arranged at or in the vicinity of animage formation position of the light beam having passed through saidfirst imaging unit; and a second imaging unit for making the light beamdeflected by said deflector to form an image on a scanned surface, andfor maintaining a conjugate relation between said reflector and saidscanned surface in a sub-scanning section, wherein said objective lensunit condenses the light beam from said light source so that thecondensed light beam is directed to said second imaging unit in a mainscanning direction, wherein said first imaging unit, having a refractivepower only in the sub-scanning direction, comprising a glass lens havinga positive refractive power in the sub-scanning direction and a resinlens having a negative refractive power in the sub-scanning direction,has as a whole a positive refractive power in the sub-scanningdirection, wherein all lens components in said second imaging unit aremade of resin, an overall refractive power thereof in the main scanningdirection being substantially null, and wherein the resin lens of thefirst imaging unit compensates for variations in the refractive power ofsaid resin lens of said second imaging unit.
 6. A scanning opticalapparatus as claimed in claim 5, wherein said first imaging unitincludes, from the light source, a glass lens having a positiverefractive power only in the sub-scanning direction and said resin lens.7. A scanning optical apparatus as claimed in claim 5, wherein saidsecond imaging unit includes a rotation-symmetric lens and a lens havinga refractive power only in the sub-scanning direction.
 8. A scanningoptical apparatus, comprising:a light source; an objective lens unit forcondensing a light beam emitted from said light source; a first imagingunit, including a first resin lens having a negative refractive power ina sub-scanning direction yet having no refractive power in a mainscanning direction, for making the light beam having passed through saidfirst imaging unit converge in the sub-scanning direction; a deflectorarranged at or in the vicinity of an image formation position of thelight beam having passed through said first imaging unit; a secondimaging unit, including a second resin lens having a positive refractivepower in the sub-scanning direction yet having no refractive power inthe main scanning direction, for making the light beam deflected by saiddeflector form an image on a scanned surface, and for maintaining asubjugate relation between said deflector and said scanned surface in asub-scanning section wherein said first resin lens and said second resinlens compensate for variation in each other's refractive power due totemperature changes.
 9. A scanning optical apparatus as claimed in claim8, wherein said first imaging unit includes, from the light source, aglass lens having a positive refractive power only in the sub-scanningdirection and said first resin lens.
 10. A scanning optical apparatus asclaimed in claim 8, wherein said second imaging unit includes, from thelight source, a glass lens having a negative refractive power, a glasslens having a positive refractive power and said second resin lens. 11.A scanning optical apparatus as claimed in claim 8, wherein a collimatedlight beam is incident on said deflector.
 12. A scanning opticalapparatus as claimed in claim 8, wherein all lens components in saidsecond imaging unit is made of resin.
 13. A scanning optical apparatusas claimed in claim 8, wherein a converging light beam is incident onsaid deflector.